Computational half-sweep explicit group Gauss–Seidel method with Caputo nonlocal arithmetic-mean approach for nonlinear time-fractional diffusion equation
This paper introduces the half-sweep 4-Point Explicit Group Gauss–Seidel (HS4EGGS) method combined with a half-sweep Caputo nonlocal arithmetic-mean discretisation for solving nonlinear time-fractional diffusion equations (NTFDEs). Designed to enhance computational efficiency and accuracy, this approach minimizes iteration counts through a half-sweep iteration strategy and accurately represents memory and hereditary properties intrinsic to fractional derivatives. The HS4EGGS method significantly reduces computational costs while maintaining precision, making it partic